Abstract

The minimum barrier (MB) distance is defined as the minimal interval of gray-level values in an image along a path between two points, where the image is considered as a vertex-valued graph. Yet this definition does not fit with the interpretation of an image as an elevation map, i.e. a somehow continuous landscape. In this paper, based on the discrete set-valued continuity setting, we present a new discrete definition for this distance, which is compatible with this interpretation, while being free from digital topology issues. Amazingly, we show that the proposed distance is related to the morphological tree of shapeswhich in addition allows for a fast and exact computation of this distance. That contrasts with the classical definition of the MB distance, where its fast computation is only an approximation.

Documents

@InProceedings{ geraud.17.ismm,
author = {Thierry G\'eraud and Yongchao Xu and Edwin Carlinet and
Nicolas Boutry},
title = {Introducing the {D}ahu Pseudo-Distance},
booktitle = {Mathematical Morphology and Its Application to Signal and
Image Processing -- Proceedings of the 13th International
Symposium on Mathematical Morphology (ISMM)},
year = {2017},
editor = {J. Angulo and S. Velasco-Forero and F. Meyer},
volume = {10225},
series = {Lecture Notes in Computer Science},
pages = {55--67},
month = may,
address = {Fontainebleau, France},
publisher = {Springer},
abstract = {The minimum barrier (MB) distance is defined as the
minimal interval of gray-level values in an image along a
path between two points, where the image is considered as a
vertex-valued graph. Yet this definition does not fit with
the interpretation of an image as an elevation map, i.e. a
somehow continuous landscape. In this paper, based on the
discrete set-valued continuity setting, we present a new
discrete definition for this distance, which is compatible
with this interpretation, while being free from digital
topology issues. Amazingly, we show that the proposed
distance is related to the morphological tree of shapes,
which in addition allows for a fast and exact computation
of this distance. That contrasts with the classical
definition of the MB distance, where its fast computation
is only an approximation.}
}